Rayleigh flow

Rayleigh flow refers to frictionless, non-Adiabatic flow through a constant area duct where the effect of heat addition or rejection is considered. Compressibility effects often come into consideration, although the Rayleigh flow model certainly also applies to incompressible flow. For this model, the duct area remains constant and no mass is added within the duct. Therefore, unlike Fanno flow, the stagnation temperature is a variable. The heat addition causes a decrease in stagnation pressure, which is known as the Rayleigh effect and is critical in the design of combustion systems. Heat addition will cause both supersonic and subsonic Mach numbers to approach Mach 1, resulting in choked flow. Conversely, heat rejection decreases a subsonic Mach number and increases a supersonic Mach number along the duct. It can be shown that for calorically perfect flows the maximum entropy occurs at M = 1. Rayleigh flow is named after John Strutt, 3rd Baron Rayleigh.

The Rayleigh flow model begins with a differential equation that relates the change in Mach number with the change in stagnation temperature, T₀. The differential equation is shown below.

Solving the differential equation leads to the relation shown below, where T₀* is the stagnation temperature at the throat location of the duct which is required for thermally choking the flow.

These values are significant in the design of combustion systems. For example, if a turbojet combustion chamber has a maximum temperature of T₀* = 2000 K, T₀ and M at the entrance to the combustion chamber must be selected so thermal choking does not occur, which will limit the mass flow rate of air into the engine and decrease thrust.

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